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JCT
2007
14 years 9 months ago
2007
We show that for any closed surface F with χ(F) −4 (or χ(F) −2), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadran...
JCT
2008
14 years 8 months ago
2008
Let {a, b, c} be a triangle in a 3-connected matroid M. In this paper, we describe the structure of M relative to {a, b, c} when, for all t in {a, b, c}, either M\t is not 3-connec...
JCT
2006
14 years 9 months ago
2006
We prove that the Kazhdan-Lusztig polynomials are combinatorial invariants for intervals up to length 8 in Coxeter groups of type A and up to length 6 in Coxeter groups of type B a...
JCT
2006
14 years 9 months ago
2006
We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic me...
JCT
2006
14 years 9 months ago
2006
One of Erdos' favourite conjectures was that any triangle-free graph G on n vertices should contain a set of n/2 vertices that spans at most n2/50 edges. We prove this when t...